From 0438468876638ceeb06c8d66fe21da0f6872b7a7 Mon Sep 17 00:00:00 2001 From: Emmanuel Fromager Date: Wed, 6 May 2020 17:55:32 +0200 Subject: [PATCH] Manu: saving work --- Revised_Manuscript/eDFT.tex | 10 +++++++++- 1 file changed, 9 insertions(+), 1 deletion(-) diff --git a/Revised_Manuscript/eDFT.tex b/Revised_Manuscript/eDFT.tex index 6e92049..3f8dd52 100644 --- a/Revised_Manuscript/eDFT.tex +++ b/Revised_Manuscript/eDFT.tex @@ -1052,7 +1052,15 @@ case, we ``deteriorate'' these states by optimizing the orbitals for the ensemble, rather than for each state separately. The reverse actually occurs for the ground state in the triensemble as $\ew{2}$ increases. The variations in the ensemble -weights are essentially linear or quadratic. They are induced by the +weights are essentially linear or quadratic. +\manurev{This can be rationalized as follows. As readily seen from +Eqs.~(\ref{eq:EI-eLDA}) and (\ref{eq:ind_HF-like_ener}), the individual +HF-like exchange does not depend explicitly on the weights, which means +that the above-mentioned variations originate from the eLDA correlation +functional [second and third terms on the right-hand side of +Eq.~(\ref{eq:EI-eLDA})]. If, for analysis purposes, we consider the +Taylor expansions around the uniform density regime in Eqs.~(\ref{eq:Taylor_exp_ind_corr_ener_eLDA}) and (\ref{eq:Taylor_exp_DDisc_term}) +}They are induced by the eLDA correlation functional, as readily seen from Eqs.~\eqref{eq:Taylor_exp_ind_corr_ener_eLDA} and \eqref{eq:Taylor_exp_DDisc_term}. In the biensemble, the weight dependence of the first